Problem: Simplify the following expression: $ r = \dfrac{1}{8} - \dfrac{7t}{6t + 4} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6t + 4}{6t + 4}$ $ \dfrac{1}{8} \times \dfrac{6t + 4}{6t + 4} = \dfrac{6t + 4}{48t + 32} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{7t}{6t + 4} \times \dfrac{8}{8} = \dfrac{56t}{48t + 32} $ Therefore $ r = \dfrac{6t + 4}{48t + 32} - \dfrac{56t}{48t + 32} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{6t + 4 - 56t }{48t + 32} $ Distribute the negative sign: $r = \dfrac{6t + 4 - 56t}{48t + 32}$ $r = \dfrac{-50t + 4}{48t + 32}$ Simplify the expression by dividing the numerator and denominator by 2: $r = \dfrac{-25t + 2}{24t + 16}$